There are four types of deontic modality, which can be expressed by the following modal expressions:

  1. Can
  2. Need not
  3. Must not
  4. Must

Out of these, 1, 3, and 4 respectively corresponds to the following nouns:

  1. Permission
  2. ???
  3. Prohibition
  4. Obligation

Is there a simple word that corresponds to type 2?

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    There are actually many more than four types of deontic modality. Every modal auxiliary has at least one, and sometimes more than one deontic sense (can can mean deontic permission or deontic ability). As for the deontic sense of need not, it means Not (Necessary p), just like don't need to or don't have to, and there doesn't appear to be a neat English term to refer to that logical situation. There often isn't; that's why Deontic gets used. – John Lawler Dec 8 '11 at 19:32
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    Can expresses ability, doesn't it? For permission, the verb is may. – Marthaª Dec 8 '11 at 19:42
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    If you prefer. Of course, preferences differ, and usages even more so. – John Lawler Dec 8 '11 at 19:50
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    Aren't Can and Need Not the same? Or do you mean Should vs Should Not – Michael Brown Dec 8 '11 at 20:43
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    @ErickRobertson: Plenty, I am sure. – Kris Dec 9 '11 at 9:05

Remission has a sense of exemption from doing something. So either of the two could serve the purpose.

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    Awesome. That is the word I was looking for. Remission was not in my vocabulary, but yes, I know the word exemption, and I think that is the perfect fit. – sawa Dec 9 '11 at 5:13
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    Remission in this sense is typically found only in legalese. We also see some occurrences in administration documents in the corporate and academic fields. I do not know if it is used as such in general literature or speech, though. – Kris Dec 9 '11 at 5:34
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    Can I expect a comment about the down vote, please? – Kris Dec 9 '11 at 7:25
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    -1: I wasn't the original downvoter, but remission doesn't mean exemption in any normal context. And as @John comments to OP, there are many "shades" of deontic modality - to me, exemption largely steps outside the entire continuum, rather than indicating the degree to which something "ought to be true". – FumbleFingers Dec 9 '11 at 13:23
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    No, but Kris is correct that "remiss" and "remit" do not, in ordinary (or even non-legal formal) usage mean "need not". I don't know about legal usage. – Ryan Haber Dec 9 '11 at 15:28

Optionality - noun form for the quality of being Left to choice; not compulsory or automatic.

Apparently this word has become significantly more common over the past 50 years.

  • Chris's answer turned out to be even better to me. Yours is still next best. – sawa Dec 9 '11 at 5:11
  • Yeah, and to keep the endings the same (which is nice), use option. – Ryan Haber Dec 9 '11 at 15:29
  • @Ryan: Per my comment to Terry's answer, I think option and election would look a bit odd alongside OP's other nouns, because they're both firmly established in somewhat different usages. – FumbleFingers Dec 9 '11 at 17:20
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    @FumbleFingers: I agree that election doesn't fit. It has a range of meanings with a shared underlying connection, but its common usage is so strong that to mean it as option is foolish. – Ryan Haber Dec 9 '11 at 19:09
  • @FumbleFingers: Option, on the other hand, strikes me as particularly good. The items of a well-formed list should be the same part of speech, at least, so that each item fulfills the same grammatical role. Option satisfies that requirement, and also has the benefit having the same ending, so there is a certain assonance. Finally, it expresses perfectly something that you may, not need not do. "There is permission to sing. There is the option to sing. There is a prohibition on singing. The is an obligation to sing." Perfect! – Ryan Haber Dec 9 '11 at 19:12

Unnecessity would fit the bill, if only it weren't obsolete. However, needlessness is not obsolete. To avoid the contrived aura, you may desire to go for a longer phrase and just use absence of necessity or lack of necessity. Or, consider using a positive-oriented word: optionality.

I gave FumbleFingers an upvote on optionality and wanted to point out that it is not only significantly more common than it was fifty years ago, it has even become more common than any of the other options:

On that basis, I think optionality deserves the cake on this issue.

  • It is actually 'absence of necessity', and I am wondering if there is a single word to express that. – sawa Dec 8 '11 at 19:04
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    Unless you allow 'needlessness'. – Barrie England Dec 8 '11 at 19:26
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    Needlessness seems to be a good choice after optionality. – sawa Dec 8 '11 at 19:46
  • 'non-necessity' seems fine to me. – Karl Knechtel Dec 9 '11 at 0:28
  • Wondering: Does needlessness convey a negative overtone like superfluousness ? – TaW May 16 '15 at 18:15

When need is used in the positive form it signifies necessity. In the negative form it signifies lack of necessity.

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    I was wondering if it is possible to say that in a single word. It looks like optionality or needlessness would give that meaning. – sawa Dec 8 '11 at 19:47
  • @sawa: I agree. I gave you the term used in grammar books. But I think you chose the correct answer wisely. – Irene Dec 8 '11 at 19:53

What about elective?

Elective: not compulsory; optional ; possible but not necessary; left to personal choice

You need to take this course = You are required to take this course (required course)

You needn't take this course = This course is elective to you (elective course)

  • The big problem with this one is when you want a noun form for the quality of being concerned with elective matters. I was a bit iffy about putting up optionality, but it's positively commonplace by comparison with electivity – FumbleFingers Dec 8 '11 at 21:19
  • @FumbleFingers Elective could be a noun form itself as in "free electives". What do you think of it? – Terry Li Dec 8 '11 at 21:32
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    Yes, I do think it's reasonable to "force" these adjectives into noun roles (you could do the same with optional). It's just they seem a bit out of place when the other three in the list are "natural" nouns formed using the -tion suffix, which we can't do with either of our offerings. Well, you could have election, I suppose, but standard usage for that word makes it a bit awkward. I certainly couldn't get away with option! :) – FumbleFingers Dec 8 '11 at 21:42

Other synonyms to consider:

  • noncompulsory
  • nonobligatory / nonobligational
  • discretionary / discretional
  • voluntary

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